During lung development, epithelial branches expand preferentially in a longitudinal direction. This bias in outgrowth has been linked to a bias in cell shape and in the cell division plane. How this bias arises is unknown. Here, we show that biased epithelial outgrowth occurs independent of the surrounding mesenchyme, of preferential turnover of the extracellular matrix at the bud tips and of FGF signalling. There is also no evidence for actin-rich filopodia at the bud tips. Rather, we find epithelial tubes to be collapsed during early lung and kidney development, and we observe fluid flow in the narrow tubes. By simulating the measured fluid flow inside segmented narrow epithelial tubes, we show that the shear stress levels on the apical surface are sufficient to explain the reported bias in cell shape and outgrowth. We use a cell-based vertex model to confirm that apical shear forces, unlike constricting forces, can give rise to both the observed bias in cell shapes and tube elongation. We conclude that shear stress may be a more general driver of biased tube elongation beyond its established role in angiogenesis. This article has an associated 'The people behind the papers' interview.